Determinant evaluations inspired by Di Francesco's determinant for twenty-vertex configurations
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910544278061056 |
|---|---|
| author | Koutschan, Christoph Krattenthaler, Christian Schlosser, Michael |
| author_facet | Koutschan, Christoph Krattenthaler, Christian Schlosser, Michael |
| contents | In his work on the twenty vertex model, Di Francesco [Electron. J. Combin. 28(4) (2021), Paper No. 4.38] found a determinant formula for the number of configurations in a specific such model, and he conjectured a closed form product formula for the evaluation of this determinant. We prove this conjecture here. Moreover, we actually generalize this determinant evaluation to a one-parameter family of determinant evaluations, and we present many more determinant evaluations of similar type - some proved, some left open as conjectures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08481 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Determinant evaluations inspired by Di Francesco's determinant for twenty-vertex configurations Koutschan, Christoph Krattenthaler, Christian Schlosser, Michael Combinatorics Statistical Mechanics Mathematical Physics Primary 15A15, Secondary 05A15, 05A19 05B45 82B20 In his work on the twenty vertex model, Di Francesco [Electron. J. Combin. 28(4) (2021), Paper No. 4.38] found a determinant formula for the number of configurations in a specific such model, and he conjectured a closed form product formula for the evaluation of this determinant. We prove this conjecture here. Moreover, we actually generalize this determinant evaluation to a one-parameter family of determinant evaluations, and we present many more determinant evaluations of similar type - some proved, some left open as conjectures. |
| title | Determinant evaluations inspired by Di Francesco's determinant for twenty-vertex configurations |
| topic | Combinatorics Statistical Mechanics Mathematical Physics Primary 15A15, Secondary 05A15, 05A19 05B45 82B20 |
| url | https://arxiv.org/abs/2401.08481 |